- Thread starter Indranil
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First, "sqrt" is not a number you can multiply ("*"). It is a function, so you write sqrt(x) to mean the square root of x.why sqrt of 1 is 1?

As I know sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what's about sqrt * 1?

The reason sqrt(4)*sqrt(4) = 4 is that the left hand side is (sqrt(4))^2, and by definition the square root is the inverse of squaring: that is, squaring undoes the square root. In general, (sqrt(x))^2 = x.

What is the square root of 1? By definition, it is the (non-negative) number whose square is 1. Since 1^2 = 1, we conclude that sqrt(1) = 1.

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To Indranil, You have been asked to use sqrt(x) which is standard function notation? Why don't you please do so?why sqrt of 1 is 1?

As I know sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what's about sqrt * 1?

If \(\displaystyle a\ge 0 \) then \(\displaystyle sqrt(a) \) is real number having the property that \(\displaystyle \left(\sqrt{a}\right)^2=a \)

So \(\displaystyle sqrt(1)\cdot sqrt(1)=\left(\sqrt{1}\right)^2=1 \)

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